Problem: Solve for $x$ and $y$ using elimination. ${2x+2y = 22}$ ${-2x+5y = 48}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $7y = 70$ $\dfrac{7y}{{7}} = \dfrac{70}{{7}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {2x+2y = 22}\thinspace$ to find $x$ ${2x + 2}{(10)}{= 22}$ $2x+20 = 22$ $2x+20{-20} = 22{-20}$ $2x = 2$ $\dfrac{2x}{{2}} = \dfrac{2}{{2}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {-2x+5y = 48}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(10)}{= 48}$ ${x = 1}$